Below is what I am trying to accomplish:

Starting at 1st level,  you gain proficiency in the Persuasion and Insight skills. In addition, the Detect Magic and Identify spells are added to your spell list. These spells count as warlock spells for you, but they don’t count against the number of warlock spells you know. You may cast these spells a combined number of times equal to your Charisma modifier without expending a pact slot, and regain all uses of this ability after a long rest. These spells can’t be replaced when you gain a level in this class.

At the moment, each spell is individually showing charges equal to my test character's charisma modifier, instead of both of them sharing the same pool of slots equal to the character's charisma modifier. Is there a way to accomplish what I am trying to do here? Here are my current settings for the feature.

Additionally, on the character's level up screen upon selecting this subclass, the above feature gives a drop-down list including the Detect Magic and Identify spells. Is there a way to simply have the spells added to the character's spell list without needing to manually select them in this drop-down menu? Because that would solve the following. In said drop-down menu, even after selecting both spells, more drop-down boxes continue to populate with the options to select Detect Magic and Identify a seemingly unlimited number of times, meaning that upon level up this feature will always be highlighted as still having options to choose akin to how the Book of Ancient Secrets invocation works. This isn't exactly the end of the world since this subclass will only ever be utilized by myself or others from my groups, but I'm a stickler for everything to work as intended.

Please help me get a better grasp of how best to implement these homebrew mechanics. Any and all constructive assistance is much appreciated.

EDIT: Fixed links.

you need to create a single action for the charges and then the user has to manually subtract the correct number of charges for whatever ability they use.

That certainly works, thanks. I just set it up this way in case I am unable to figure out exactly what I'm going for.

So from what I am finding there doesn't seem to be a way to do it so upon clicking the spell on the spell list it uses one of the charges like it does when they both show separate charges? As in the button to use the spell on the spell list shows up at 1U, which then automatically subtracts a use from the shared pool of uses?

Correct, I do not believe there is a way to do that.

In that case, thank you very much for your assistance! It'll do for the time being.

You could fake it by putting the spells on a magic item with the charges.

The thing is PC’s don’t have “charges” since they have spell slots. It would be nice if we could use “charges” on characters though.

In regards to the way Houligan suggested: That’s also how official features with similar designed were coded. If you’ll notice, when the player taps the relevant spell on their sheet, at the top of the slideout it lists the name of the feature that grants that spell. That’s a link to the feature entry on their character sheet, and the attached action with the limited use counter is also attached to that feature. So they can tick off the uses right there as a relatively convenient shortcut. 

Thanks for the clarification. I am using Houligan's workaround, the same one you are reinforcing as the way to go. It'll have to do. Now all I have to wait for is the ability to create homebrew Eldritch Invocations that are actually selectable via the level-up menu. I've got three that go with the subclass to start, with more coming based on what pact boon the player might take.

Make an another class feature called “Alternative Invocations” with a not that the total doesn’t change, only additional options are added and then implement each one using “options” attached to the feature. That’s the closest you can get.